Softening the steps to gigantism in sauropod dinosaurs through the evolution of a pedal pad

How sauropod dinosaurs were able to withstand the forces associated with their immense size represents one of the most challenging biomechanical scenarios in the evolution of terrestrial tetrapods, but also one lacking robust biomechanical testing. Here, we use finite element analyses to quantify the biomechanical effects of foot skeletal postures with and without the presence of a soft tissue pad in sauropodomorphs. We find that none of the models can maintain bone stresses that fall within optimal bone safety factors in the absence of a soft tissue pad. Our findings suggest that a soft tissue pad in sauropods would have reduced bone stresses by combining the mechanical advantages of a functionally plantigrade foot with the plesiomorphic skeletally digitigrade saurischian condition. The acquisition of a developed soft tissue pad by the Late Triassic–Early Jurassic may represent one of the key adaptations for the evolution of gigantism that has become emblematic of these dinosaurs.

for the bones and cartilaginous capsules and of 1 mm for the soft tissue pad due to its comparatively larger volume size).
Materials properties -Due to the lack of data on tissue material properties of anatomical constituents in fossil specimens, linear elasticity, homogeneity and isotropy were assumed for each model. To validate the tested material properties values, we surveyed 130 + FEA papers performed on extant and extinct taxa to document the material properties (i.e., Young's modulus and Poisson ratio) assigned to a variety of bones and soft tissues in the literature (Data S1).
(1) Bones: The vast majority of FE analyses in palaeontology suggests that bones of many dinosaurs (and other archosaurs) appear analogous to the Haversian bones of fast-growing bovine mammals (75)(76)(77). In reality, however, the review of the literature denotes the wide range of material properties values attributed to bones in distinct fossil taxa (Data S1). Without further histological insights about the sauropod pedal elements, we assigned a proxy E value of 10,000 MPa and a ν value of 0.3 to each bone model, representative of the most commonly used E value for bones in the literature.
Such a variation in reported cartilage properties is likely contingent on multiple factors, including ontogeny, species, size, or a specific region of a joint, among other (94,95). Consequently, a sensitivity analysis was performed to assess how variations in E values of the cartilaginous capsules affect stresses distribution. Three values of Young's modulus were assigned to our pseudo-cartilages, including: 100 MPa (C1), 10 MPa (C2), and 1 MPa (C3) (Figs. S13-S18). In all cases, a constant Poisson's ratio of 0.4 was assigned, representative of the most commonly E values for cartilages among living taxa (Data S1).
(3) Pseudo soft tissue pads: Among living terrestrial tetrapods, only a few organisms seem to possess padding tissues within the palmar/plantar regions of their autopodia that may resemble the structure investigated here. Previous studies interpreted these structures to exhibit nonlinear, viscoelastic behaviours (47,80,107), somewhat similar to cartilage, and consisting of fibrous connective tissues (34,48,108) (Data S1). Owing perhaps on the intra-and inter-variability of these tissues through ontogeny and taxa (34,80), detailed material properties of such padding tissues reveal equivocal Young's modulus values in the literature (109,110) (Data S1). To avert making unfounded assumptions, a sensitivity analysis was performed to assess how variations in in the soft tissue pad elastic moduli affect stresses distributions. Four values of Young's modulus, ranging from highly viscoelastic to more cartilaginous materials, were assigned to our pseudo soft tissue pad, including: 0.1 MPa (F1), 1 MPa (F2), 10 MPa (F3), and 100 MPa (F4) (Figs. S19-S24).
In all cases, a constant Poisson's ratio of 0.49 was used, representing the only value attributed to fatty tissues among living taxa in the literature (Data S1).
Boundary conditions -We replicated the weight-bearing phase of locomotion by assuming that the sauropod pes was in complete contact with the substrate. To simulate weight-bearing in the Cartesian system, the dorsal surface of the pes was loaded vertically in the inverse direction of the z-axis (i.e., towards the substrate), and its plantar surface, assumed in interaction with the ground, was constrained (with the exception of digit V, which did not interact with the substrate in most postures). Nonetheless, a series of sensitivity analyses was conducted to test the effects of constraint and loading conditions on each model. (2) Loading: Forces were applied to surface nodes at the proximal surfaces of each metatarsal and the proximal surface of the soft tissue pad when included (Fig. S28). An initial vertical force of 10,000 N (L1) was used as a proxy between our FEMs to permit direct comparison between each sauropodomorph taxon and with our simulated elephant pes. Force estimates originate from force estimations in living elephants, corresponding to an animal with a body mass of 3,000-4,000 kg (23) (Table S7), which was therefore used in this discourse for our simulated elephant pes. In FEMs that included a hypothetical pad, a sensitivity analysis was performed to assess how the applied forces affect stress distributions. Two sets of applied forces were investigated, including: Ultimately, more physiologically realistic loads were tested for each fossil taxon (L2) using the body mass estimation for each of our specimen. In palaeontology, the 'body mass scaling method' is generally used to estimate the body mass of a fossil (41). This method is based on the empirical scaling relationship of stylopodial circumferences (i.e., humerus and femur) derived from extant tetrapods. As described previously (41): Appendix S1, masses in kilograms are estimated using femoral and humeral circumferences (FC and HC, respectively), which are expressed within the following equations: Where for bipedal taxa: = 2.749 × log 10 ( × 2 0.5 ) − 1.104 (2) and for quadrupedal taxa: = 2.749 × log 10 ( + ) − 1.104 (3) In this study, the body masses of P. engelhardti, D. carnegii, C. sp., and G. brancai were estimated following the equations above (Table S7). Conversely, the estimation of R. brownei body mass was hampered because this specimen only preserves a partial femur. To base our inferences on empirical data, a regression plot was generated using stylopodial circumferences of all known sauropods (41) (Fig. S5). We estimated that the humerus circumference of R. brownei fitted in a range of 450-600 cm, using its known femur circumference (i.e., 696 mm), ( Fig. S5 and Table S7). The body mass of R. brownei was therefore projected to be within a range of 20,000-28,000 kg (mean of 24,000 kg) (Tables S7). Finally, all loading forces were calculated by multiplying the estimated body mass of each specimen (m, in kg) with the gravitational acceleration (i.e., g = 9.834 m/s 2 ) to obtain a force measurement in Newtons (N). The resulting force was divided by four under the assumption that loads were equally distributed between the four autopodia during the support phase (i.e., = ; with = 1 4 ) (Table S7). However, this load regime may be an underestimation in some of our specimens examined considering that the hindlimbs have been proposed to bear most of the body weight during locomotion in more derived forms (5,111).

Expanded Results
Brief overview -This section provides an extended summary of the results for each sensitivity analysis. It should be noted that most of the sensitivity analyses were undertaken on all sauropodomorph specimens. However, some features (e.g., pad outlines, constraints) were only investigated in one sauropod taxon (herein R. brownei), our non-sauropod (out-group) exemplar  (29)).
In unguligrady, only the distal portion of the ungual of each digit firmly contacts the substrate, resulting in higher von Mises stresses in the distalmost phalanges compared to the other morphotypes. These results suggest that the large mediolaterally compressed unguals, combined with their bevelled and concave articular facets, are not anatomically adapted for loading the tips of the unguals alone. Additionally, among modern unguligrade tetrapods, the distalmost phalanges include hoofed and keratinous-covered material that engage the substrate via a flat distal surface (e.g., Equidae, among other unguligrade artiodactyls; (112,113) (36,96). Thus, we conclude that the plantigrade and unguligrade configurations in our specimens are unlikely given their anatomy. These results corroborate and supplement a previous study (29).

Soft tissue pad outlines
The sensitivity analyses of varying the outlines of the soft tissue pad (PAD1 and PAD2) were were observed in the simulated elephant pes (Fig. S18). Therefore, we chose to apply an E value of 100 MPa (C1) to the cartilaginous capsule of all FEMs for ease of comparison and replication.

Soft tissue pad properties
We conducted sensitivity analyses to test the effect of varying the soft tissue pad E values on bone stresses (Figs. S19-S23). We found that soft tissue pad properties did not impact bone stresses

Constraints: Skeletal without soft tissue pad
We tested the effect of constraints on bone stresses in R. brownei and the simulated elephant pes ( Fig. S25). We found that constraint location had an effect on bone stress magnitudes but not on stress distribution. All FEMs showed the highest concentrations of von Mises stresses in the lateral digits, particularly within the shaft of metatarsals III-IV. Strikingly, constraints BCs 1-3 (i.e., constraining nodes in the plantar surfaces of the most distal elements of the pes) recorded the highest concentration of von Mises stresses than constraints BCs 4-6 (i.e., constraining nodes in the plantar surfaces of all the elements in contact with the ground). Similar outcomes were observed in the simulated elephant pes where constraining the plantar surfaces of all the elements in contact with the ground decreased von Mises bone stresses (Fig. S27). We applied the more cost-effective condition BC5 for all other taxa in the main text for ease of comparison and replication as strain results between BC5 and BC6 were similar, yet BC6 increased substantially computational time in our FEA.

Constraints: Skeletal with soft tissue pad
We tested the boundary conditions on skeletal morphotypes with a soft tissue pad in R. brownei and the simulated elephant pes (Fig. S26). Irrespective of the type of constraints, the results showed a reduction in bone stresses for each postural morphotype compared to loading the skeletal postures alone, with maximum von Mises stresses < 100 MPa. Constraints BCs' 1-2 (i.e., constraining the nodes on the plantar surfaces of the soft tissue pad alone) recorded marginally reduced stress magnitudes compared to constraints BCs' 3-4 (i.e., constraining the nodes on the plantar surfaces of the digits and the soft tissue pad). Similar outcomes were observed in the simulated elephant pes (Fig. S27). Therefore, we chose to assign the more realistic condition BC4' to all other specimens by constraining the plantar surfaces of all the components in complete contact with the substrate (i.e., pad + bones and cartilages) for ease of comparison and replication.

Applied forces on soft tissue pad
We tested the loading conditions on the skeletal postural morphotype with a soft tissue pad in R.
brownei and the simulated elephant pes (Fig. S28). Irrespective of the loading conditions, the results showed a reduction in bone stresses for all postural morphotypes with a soft tissue pad compared to loading the skeletal postures alone, with maximum von Mises stresses < 100 MPa.
Loading condition L1 (i.e., an applied force on the proximal surfaces of the metatarsals and the soft tissue pad) recorded lower concentrations in von Mises stresses compared to L1B (i.e., an applied force on the proximal surfaces of the metatarsals). Moreover, the application of L1B bended the metatarsals in the dorsoplantar direction. Similar outcomes were observed in the simulated elephant pes. Therefore, we chose to apply the loading conditions L1 and L2 to all FEMS for ease of comparison and replication.

Applied forces: proxy vs. realistic -Skeletal without soft tissue pad
The results showed that the applications of more physiologically realistic loading forces on our models without a pad retained the same stress distribution but differed in stress magnitude compared to our proxy load (Figs. S29-S33).

Applied forces: proxy vs. realistic -Skeletal with soft tissue pad
As above, the results showed that the applications of more physiologically realistic loading forces on our models with a pad retained the same stress distribution but differed in stress magnitude compared to our proxy load (Figs. S29-S33). These results are expected because each model has been subjected to strictly similar conditions. Hence, variations of the loading forces should not change the stress distribution and only affect stress magnitude.

Additional notes: Trend towards a reduction and loss of the number of autopodial phalanges in sauropod evolutionary history
The uniform pattern of stress recorded between FEMs may correlate with the conspicuous trend towards a reduction and loss of the number of autopodial phalanges in sauropod evolutionary history (18,30,40). Given that a decrease in von Mises stresses is recorded on the distal phalanges when a pad is included, it is proposed that the shock absorbing aptitude of a soft tissue pad would have impeded the weight-bearing purposes of the distalmost phalanges. This mechanical state could explain the general reduction in the size of the phalanges (18), making them susceptible to be lost throughout the course of sauropod evolution. (1, 17,22,29,34,[81][82][83][84][85]89) Table S6 for details on the respective number of elements.                   (legend on next page)

54
(legend on next page)

62
(legend on next page) (44,45) Table S8. Note: We purposely varied the von Mises stress scale to illustrate better the individual details of each graphic.  Table S8. Note: We purposely varied the Maximum Principal stress scale to illustrate better the individual details of each graphic